Papers by Berry Schoenmakers
Springer eBooks, 2011
O-notation is a way of expressing the relationship between the growth rates of two functions.
Springer eBooks, Sep 9, 2006
Springer eBooks, Sep 9, 2006
Encyclopedia of Cryptography and Security
Springer eBooks, Sep 9, 2006
Chapman and Hall/CRC eBooks, Nov 20, 2009
Springer eBooks, Sep 9, 2006
No abstract
Computer, Sep 1, 2011
The SecureSCM project demonstrates the practical applicability of secure multiparty computation t... more The SecureSCM project demonstrates the practical applicability of secure multiparty computation to online business collaboration. A prototype supply-chain management system protects the confidentiality of private data while rapidly adapting to changing business needs.
Lecture Notes in Computer Science, 2008
ABSTRACT The algebraic setting for threshold secret sharing scheme can vary, dependent on the app... more ABSTRACT The algebraic setting for threshold secret sharing scheme can vary, dependent on the application. This algebraic setting can limit the number of participants of an ideal secret sharing scheme. Thus it is im- portant to know for which thresholds one could utilize an ideal threshold sharing scheme and for which thresholds one would have to use non- ideal schemes. The implication is that more than one share may have to be dealt to some or all parties. Karnin, Greene and Hellman con- structed several bounds concerning the maximal number of participants in threshold sharing scheme. There has been a number of researchers who have noted the relationship between k-arcs in projective spaces and ideal linear threshold secret schemes, as well as between MDS codes and ideal linear threshold secret sharing schemes. Further, researchers have constructed optimal bounds concerning the size of k-arcs in projective spaces, MDS codes, etc. for various nite elds. Unfortunately, the ap- plication of these results on the Karnin, Greene and Hellamn bounds has not been widely disseminated. Our contribution in this paper is revisit- ing and updating the Karnin, Greene, and Hellman bounds, providing optimal bounds on the number of participants in ideal linear threshold secret sharing schemes for various nite elds, and constructing these bounds using the same tools that Karnin, Greene, and Hellman intro- duced in their seminal paper. We provide optimal bounds for the maximal number of players for a t out of n ideal linear threshold scheme when t = 3, for all possible nite elds. We also provide bounds for innitely many t and innitely many elds and a unifying relationship between this problem and the MDS (maximum distance separable) codes that shows that any improvement on bounds for ideal linear threshold secret sharing scheme will impact bounds on MDS codes, for which there is a number of conjectured (but open) problems.
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Papers by Berry Schoenmakers